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Exploring Statistical and Nonclassical Properties in Cavity Optomechanical Systems Applying Arbitrary Single-mode Light States

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Abstract

This article theoretically investigates the optomechanical system with one movable mirror, initially set in an arbitrary single-mode cavity and a Fock state for the mechanical mode. The study extracts the system’s wave function and derives the general equations governing numerous statistical and nonclassical properties. Among the statistical features explored are the average phonon number, its fluctuations, as well as the average position and momentum of the movable mirror. Intriguingly, it becomes apparent that the average number of phonons is contingent upon the mean-square photon number, whereas the average position and momentum directly correlate with the average photon number. Moreover, we demonstrate that while maintaining the mean number of photons, it is possible to achieve an unlimited mean number of phonons. The examined nonclassical characteristics of the mechanical mode, encompassing sub-Poissonian statistics, squeezing, linear entropy (entanglement), and the Wigner distribution. Interestingly, achieving a sub-Poissonian distribution for phonons proves unattainable with vacuum, yet becomes feasible with higher Fock phonon states. Conversely, the possibility of squeezing remains inaccessible across all input cavity states. The analysis further applies the established general formulas to five distinct states: the Fock state, squeezed vacuum state, coherent state, Mth coherent states, and a specific superposition of two Fock states.

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References

  1. Chang, L., Jiang, X.S., et al.: Parity time symmetry and variable optical isolation in active passive-coupled microresonators. Nat. Photon. 8, 524 (2014)

    Article  ADS  Google Scholar 

  2. Walter, S., Marquardt, F.: Classical dynamical gauge fields in optomechanics. New J. Phys. 18, 113029 (2016)

    Article  ADS  Google Scholar 

  3. Hill, J.T., Safavi-Naeini, A.H., Chan, J., Painter, O.: Coherent optical wavelength conversion via cavity optomechanics. Nat. Commun. 3, 1196 (2012)

    Article  ADS  Google Scholar 

  4. Akram, M.J., Khan, M.M., Saif, F.: Tunable fast and slow light in a hybrid optomechanical system. Phys. Rev. A 92, 023846 (2015)

    Article  ADS  Google Scholar 

  5. Jiang, C., Cui, Y., et al.: Phase-controlled amplification and slow light in a hybrid optomechanical system. Opt. Express 27, 30473 (2019)

    Article  ADS  Google Scholar 

  6. Zhao, J., Wu, L., et al.: Phase-controlled pathway interferences and switchable fast-slow light in a cavity-magnon polariton system. Phys. Rev. Applied 15, 024056 (2021)

    Article  ADS  Google Scholar 

  7. Mancini, S., Man’ko, V.I., Tombesi, P.: Ponderomotive control of quantum macroscopic coherence. Phys. Rev. A 55, 3042 (1997)

    Article  ADS  Google Scholar 

  8. Bose, S., Jacobs, K., Knight, P.L.: Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56, 4175 (1997)

    Article  ADS  Google Scholar 

  9. Rips, S., Hartmann, M.J.: Quantum information processing with nanomechanical qubits. Phys. Rev. Lett. 110, 120503 (2013)

    Article  ADS  Google Scholar 

  10. Liao, Q.H., Xiao, X., Nie, W.J., Zhou, N.R.: Transparency and tunable slow-fast light in a hybrid cavity optomechanical system. Opt. Express 28, 4 (2020)

    Article  Google Scholar 

  11. Teufel, J.D., Donner, T., Li, D., et al.: Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359 (2011)

    Article  ADS  Google Scholar 

  12. Li, L., Nie, W.J., Chen, A.: Transparency and tunable slow and fast light in a nonlinear optomechanical cavity. Sci. Rep. 6, 35090 (2016)

    Article  ADS  Google Scholar 

  13. Fonseca, P.Z.G., Aranas, E.B., et al.: Nonlinear dynamics and strong cavity cooling of levitated nanoparticles. Phys. Rev. Lett. 117, 173602 (2016)

    Article  ADS  Google Scholar 

  14. Gu, W.J., Li, G.X.: Quantum interference effects on ground-state optomechanical cooling. Phys. Rev. A 87, 025804 (2013)

    Article  ADS  Google Scholar 

  15. Roque, T.F., V.-Barranco, A.: Coherence properties of coupled optomechanical cavities. J. Opt. Soc. Am. B. 31, 1232 (2014)

    Article  ADS  Google Scholar 

  16. Safavi-Naeini, A.H., Mayer Alegre, T.P., et al.: Electromagnetically induced transparency and slow light with optomechanics. Nature 472, 69 (2011)

    Article  ADS  Google Scholar 

  17. Ma, Y.-Q., Danilishin, S.L., et al.: Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction. Phys. Rev. Lett. 113, 151102 (2014)

    Article  ADS  Google Scholar 

  18. Glauber, R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Sudarshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Banerjee, S., Srikanth, R.: Phase diffusion in quantum dissipative systems. Phys. Rev. A 76, 062109 (2007)

    Article  ADS  Google Scholar 

  21. Yuan, Z., Kardynal, B.E., Stevenson, R.M., et al.: Electrically driven single-photon source. Science 295, 102 (2002)

    Article  ADS  Google Scholar 

  22. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Hillery, M., OĆonnell, R.F., Scully, M.O., et al.: Distribution functions in physics: fundamentals. Phys. Rep. 106, 121 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  24. Nielsen, M., Chuang, I.L.: Quantum information and quantum computation. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  25. Bennett, C.H., Brassard, G., Crépeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Liang, X., Guo, Q., Yuan, W.: Nonclassical properties of an opto-mechanical system initially prepared in N-headed cat state and number state. Int. J. Theor. Phys. 58, 58 (2019)

    Article  MATH  Google Scholar 

  28. Liao, Q.H., Nie, W.J., et al.: Properties of linear entropy of the atom in a tripartite cavity-optomechanical system. Laser Phys. 26, 055201 (2016)

    Article  ADS  Google Scholar 

  29. Nadiki, M.H., Tavassoly, M.K.: Collapse-revival in entanglement and photon statistics: the interaction of a three-level atom with a two-mode quantized field in cavity optomechanics. Laser Phys. 26, 125204 (2016)

    Article  ADS  Google Scholar 

  30. Sekatski, P., Aspelmeyer, M., Sangouard, N.: Macroscopic optomechanics from displaced single-photon entanglement. Phys. Rev. Lett. 112, 080502 (2014)

    Article  ADS  Google Scholar 

  31. Grosso, N.F., Lombardo, F.C., Villar, P.I.: Photon generation via the dynamical Casimir effect in an optomechanical cavity as a closed quantum system. Phys. Rev. A 100, 062516 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  32. Dehghani, A., Mojaveri, B., Aryaie, M.: Quantum dynamics of a f-deformed opto-mechanical system. Int. J. Theor. Phys. 62, 5 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  33. Alam, N., et al.: Bose-condensed optomechanical-like system and a Fabry-Perot cavity with one movable mirror: quantum correlations from the perspectives of quantum optics. Eur. Phys. J. D 73, 139 (2019)

    Article  ADS  Google Scholar 

  34. Li, H.-M., et al.: Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors. Chin. Phys. B 32, 014202 (2023)

    Article  ADS  Google Scholar 

  35. Rastegarzadeh, M., Tavassoly, M.K., Nadiki, M.H.: Single-photon blockade in a hybrid optomechanical system involving two qubits in the presence of phononic number and coherent states. Quan. Inf. Proc. 22, 95 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  36. Galland, C., Sangouard, N., Piro, N., Gisin, N., Kippenberg, T.J.: Heralded single-phonon preparation, storage, and readout in cavity optomechanics. Phys. Rev. Lett. 112, 143602 (2014)

    Article  ADS  Google Scholar 

  37. Glauber, R.J.: The quantum theory of optical coherence. Phys. Rev. 130, 2529 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  38. Alam, N., Mandal, K., Pathak, A.: Higher-order nonclassical properties of a shifted symmetric cat state and a one-dimensional continuous superposition of Coherent states. Int. J. Theor. Phys. 57, 3443 (2018)

    Article  MATH  Google Scholar 

  39. Othman, A.: The Mth coherent state. Int. J. Theor. Phys. 58, 2451 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  40. Othman, A.A.: Mth coherent state induces patterns in the interaction of a two-level atom in the presence of nonlinearities. Int. J. Theor. Phys. 60, 1574 (2021)

    Article  MATH  Google Scholar 

  41. Nahla, A.A., Othman, A.A.: Effect of Mth coherent state on the interaction between two two-level atoms and two-mode quantized field. J. Taibah Univ. for Sci. 16, 1053 (2022)

    Article  Google Scholar 

  42. Uria, M., Solano, P., H.-Avigliano, C.: Deterministic generation of large fock states. Phys. Rev. Lett. 125, 093603 (2020)

    Article  ADS  Google Scholar 

  43. Wu, L.-A., Kimble, H.J., Hall, J.L., Wu, H.: Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986)

    Article  ADS  Google Scholar 

  44. Gerry, C.C., Knight, P.L.: Introductory quantum optics. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  45. Zhang, W.-M., Feng, D.H., Gilmore, R.: Coherent states: theory and some applications. Rev. Mod. Phys. 62, 867 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  46. Vogel, K., Akulin, V.M., Schleich, W.P.: Quantum state engineering of the radiation field. Phys. Rev. Lett. 71, 1816 (1993)

    Article  ADS  Google Scholar 

  47. M.-Cessa, H.: Generation and properties of superpositions of displaced Fock states. J. Mod. Opt. 42, 1741 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Karimi, A.: Construction of the superposition of displaced Fock states and entangled displaced Fock states. Int. J. Theor. Phys. 56, 2709 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  49. Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)

    Article  ADS  Google Scholar 

  50. Mandel, L.: Sub-poissonian photon statistics in resonance fluorescence. Opt. Lett. 4, 205 (1979)

    Article  ADS  Google Scholar 

  51. Caves, C.M., Schumaker, B.L.: New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states. Phys. Rev. A 31, 3068 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  52. Zurek, W.H., Habib, S., Paz, P.J.: Coherent states via decoherence. Phys. Rev. Lett. 70, 1187 (1993)

    Article  ADS  Google Scholar 

  53. Werner, R.F.: In: Springer tracts in modern physics, 173. Springer, Heidelberg (2001)

    Google Scholar 

  54. Agarwal, G.S.: Quantum optics. Cambridge University Press, Cambridge (2013)

    MATH  Google Scholar 

  55. Tanas, R., Murzakhmetov, B.K., Gantsog, T., Chizhov, A.V.: Phase properties of displaced number states. Quantum Opt. 4, 1 (1992)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

The author acknowledges the financial support from Taibah University.

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  1. Department of Physics, Faculty of Science, Taibah University, Al Madinah Al Munawwarah, Saudi Arabia

    Anas Othman

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I, Anas Othman, am the sole author of this article and have performed all the research, data analysis, and writing presented in the manuscript.

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Othman, A. Exploring Statistical and Nonclassical Properties in Cavity Optomechanical Systems Applying Arbitrary Single-mode Light States. Int J Theor Phys 62, 242 (2023). https://doi.org/10.1007/s10773-023-05500-y

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